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Steerable CNNs
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It has long been recognized that the invariance and equivariance properties of a representation are critically important for success in many vision tasks. In this paper we present Steerable Convolutional Neural Networks, an efficient and flexible class of equivariant convolutional networks. We show that steerable CNNs achieve state of the art results on the CIFAR image classification benchmark. The mathematical theory of steerable representations reveals a type system in which any steerable representation is a composition of elementary feature types, each one associated with a particular kind of symmetry. We show how the parameter cost of a steerable filter bank depends on the types of the input and output features, and show how to use this knowledge to construct CNNs that utilize parameters effectively.
Forward citations
Cited by 11 Pith papers
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Rotation Equivariant Mamba for Vision Tasks
EQ-VMamba adds rotation-equivariant cross-scan and group Mamba blocks to enforce end-to-end rotation equivariance, yielding better rotation robustness, competitive accuracy, and roughly 50% fewer parameters than non-e...
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A Unified Framework for Vision Transformers Equivariant to Discrete Subgroups of $\mathrm{O}(2)$
Constructs G-equivariant ViTs for arbitrary discrete G ≤ O(2), proves H ≤ G implies G-models embed into H-models and single-head equivariant attention realizes all ordinary G-equivariant maps, introduces D6 hexagonal ...
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A Unified Framework for Vision Transformers Equivariant to Discrete Subgroups of $\mathrm{O}(2)$
A unified family of vision transformers equivariant to arbitrary discrete subgroups of O(2), with embedding and expressivity theorems, a D6 construction using hexagonal patches, and experiments on aerial images in low...
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Graph Neural Networks in the Wilson Loop Representation of Abelian Lattice Gauge Theories
A gauge-invariant GNN using Wilson loops as inputs accurately predicts observables and simulates dynamics in Z2 and U(1) lattice gauge models.
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Equivariant Volumetric Grasping
A novel tri-plane equivariant volumetric grasp model adapts GIGA and IGD planners with flow matching and deformable attention to achieve higher real-time performance than non-equivariant baselines.
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Algebraic Priors for Approximately Equivariant Networks
Proves regular representation must appear in latent space of finite-group equivariant encoders and enforces it via auxiliary loss to match specialized equivariant models without added parameters.
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Mirror-Fusion Attention for Reflection-Aware Self-Supervised Representation Learning
MFASSL adds mirror-paired views, a lightweight Mirror-Fusion Attention module, and reflection-consistency losses to improve SSL on bilateral data with ~2.7% extra parameters.
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When do complex-valued neural networks help? A study of representation, geometry, and optimization
Complex-valued networks show task-dependent gains over real baselines on phase-sensitive data like PSK but not QAM, with large benchmark gaps often caused by hyperparameter instability rather than inherent superiority.
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Rotation Equivariant Convolutions in Deformable Registration of Brain MRI
Rotation-equivariant convolutions in deformable brain MRI registration networks deliver higher accuracy with fewer parameters, greater robustness to rotations, and better performance on limited training data.
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Adaptive Canonicalization with Application to Invariant Anisotropic Geometric Networks
Adaptive canonicalization selects input canonical forms by maximizing network predictive confidence to yield continuous symmetry-preserving models with universal approximation for equivariant geometric networks.
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Leveraging Kernel Symmetry for Joint Compression and Error Mitigation in Edge Model Transfer
A DoF codec exploiting kernel symmetries compresses neural models for noisy channels and projects received weights onto the symmetry subspace to mitigate errors, outperforming pruning on MNIST and CIFAR-10.
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